Related papers: About a result of S.M. Kozlov
We show that the already known results for a composition operator to have closed range on H2 (Cima, Thomson, and Wogen (1974), Zorboska (1994)) can be extended to Hp for p>0 .
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
An analysis of cosmological mixed dark matter models in spatially flat Friedmann Universe with zero $\Lambda$-term is presented. We argue that the introduction of cosmic gravity waves helps to satisfy observational constraints. The analysis…
This work prolongs recent investigations by Bergeron et al [see 2012 J. Phys. A: Math. Theo. 45 244028] on new SUSYQM coherent states for P\"oschl-Teller potentials. It mainly addresses explicit computations of eigenfunctions and spectrum…
In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). Using these representations,…
In the realm of the $\omega$CDM cosmological model with quiescence or quintessence as the dark energy, characterized by $\omega>-1$, there exists a fixed value of $H(z)$ at $z=-1$, devoid of dependency on other cosmological parameters. To…
We classify the asymptotic densities of the $\Delta^0_2$ sets according to their level in the Ershov hierarchy. In particular, it is shown that for $n \geq 2$, a real $r \in [0,1]$ is the density of an $n$-c.e.\ set if and only if it is a…
Given a semiring with a preorder subject to certain conditions, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is a compact Hausdorff space together with a map from the semiring to the ring of continuous…
Recent work by Hintz--Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schr\"odinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic…
Let $(M,g)$ be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on $M$. Let $\epsilon >0$. We study the semiclassical measures…
The behavior of simple eigenvalues of Aharonov-Bohm operators with many coalescing poles is discussed. In the case of half-integer circulation, a gauge transformation makes the problem equivalent to an eigenvalue problem for the Laplacian…
We prove a new off-diagonal asymptotic of the Bergman kernels associated to tensor powers of a positive line bundle on a compact K\"ahler manifold. We show that if the K\"ahler potential is real analytic, then the Bergman kernel accepts a…
The dynamic feature of monochromatic bi-modal chaotic optical field, enriched with orthogonally-polarized basis-modes propagating collinearly and undergoing Degenerate Parametric Amplification, is investigated to demonstrate Squeezing in…
We establish the asymptotic behaviour of the ratio $h^\prime(0)/h(0)$ for $\lambda\rightarrow\infty$, where $h(r)$ is a solution, vanishing at infinity, of the differential equation $h^{\prime\prime}(r) = i\lambda \omega (r) h(r)$ on the…
We study a minimizing problem associated with the singular problem \[ \left\{ \begin{array} [c]{ll} -\operatorname{div}\left( \left\vert \nabla u\right\vert ^{p-2}\nabla u\right) =\lambda u^{-1} & \mathrm{in\ }\Omega\\ u>0 & \mathrm{in\…
We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone…
The asymptotic behaviors of the integrated density of states $N(\lambda)$ of Schr\"odinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading…
We consider the semiclassical operator $\hat{H}(\epsilon,h):=H_{0}(hD_{x})+\epsilon \tilde{P}_{0}$ on $L^{2}(\mathbb{R}^{l})$, where the symbol of $\hat{H}(\epsilon,h)$ corresponds to a perturbed classical Hamiltonian of the form:…
In this paper, we considered the spectrum of the Dirichlet Laplacian $\Delta_\epsilon$ on $\Omega_\epsilon=\{(x,y): -l_1<x<l_2, 0<y<\epsilon h(x)]\}$ where $ l_1,l_2>0$ and $h(x)$ is a positive analytic function having $0$ the only point…
We quantify the internal structure of near-threshold bound, virtual, and resonance states in systems where Coulomb and short-range interactions coexist by evaluating the compositeness. Using the Coulomb-modified effective range expansion,…